Related papers: Some virtually poly-free Artin groups

We prove that an Artin group splits over infinite cyclic subgroups if and only if its defining graph has a separating vertex, and explicitly construct a JSJ decomposition over infinite cyclic subgroups for all Artin groups. We then use…

We show that the fundamental group of a geometrically clean graph of finite rank free groups does not need to be virtually compact special, answering a question of Wise. This implies that the class of the virtually VH-clean graphs of finite…

We study the class N of graphs, the right-angled Artin groups defined on which do not contain surface subgroups. We prove that a presumably smaller class N' is closed under amalgamating along complete subgraphs, and also under adding…

Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.

We give a necessary and sufficient condition for a 2-dimensional or a three-generator Artin group $A$ to be (virtually) cocompactly cubulated, in terms of the defining graph of $A$.

We give an alternative proof to the fact that if the square of the infinite radical of the module category of an Artin algebra is equal to zero then the algebra is of finite type by making use of the theory of postprojective and…

We introduce a new model of random Artin groups. The two variables we consider are the rank of the Artin groups and the set of permitted coefficients of their defining graphs. The heart of our model is to control the speed at which we make…

Let $G$ be a subgroup of ${\rm PGL}_2({\mathbb F}_q)$, where $q$ is any prime power, and let $Q \in {\mathbb F}_q[x]$ such that ${\mathbb F}_q(x)/{\mathbb F}_q(Q(x))$ is a Galois extension with group $G$. By explicitly computing the Artin…

Finite type invariants (also known as Vassiliev invariants) of pure braids are considered from a group-theoretic point of view. New results include a construction of a universal invariant with integer coefficients based on the Magnus…

Let G be a free group in a variety of groups, but G is not absolutely free. We prove that the group of automorphisms Aut(G) is linear iff G is a virtually nilpotent group.

We prove Artin's axioms satisfy a compatibility for composition of 1-morphisms of stacks in groupoids. Consequently, some natural stacks in groupoids are algebraic, including a common generalization of Vistoli's Hilbert stack and the stack…

We obtain a criterion for the automorphism group of an affine toric variety to be connected in combinatorial terms and in terms of the divisor class group of the variety. The component group of the automorphism group of a non-degenerate…

We prove that two co-Hopfian finitely generated virtually free groups are elementarily equivalent if and only if they are isomorphic. We also prove that co-Hopfian finitely generated virtually free groups are homogeneous in the sense of…

We present a complete rewriting system for twisted right-angled Artin groups. Utilizing the normal form coming from the rewriting system, we provide applications that illustrate differences and similarities with right-angled Artin groups,…

In this article, we study the property of being equationally Artinian in groups. We prove that a finite extension of an equationally Artinian group is again equationally Artinian. We also show that a quotient of an equationally Artinian…

We prove the $\Sigma^1$-conjecture for two families of Artin groups: Artin groups such that there exists a prime number $p$ dividing $\frac{l(e)}{2}$ for every edge $e$ with even label $>2$ and balanced Artin groups. The family of balanced…

We show that a triangle Artin group $\text{Art}_{MNP}$ where $M\leq N\leq P$ splits as an amalgamated product or an HNN extension of finite rank free groups, provided that either $M>2$, or $N>3$. We also prove that all even three generator…

We determine the image of the Artin groups of types B and D inside the Iwahori-Hecke algebras, when defined over finite fields, in the semisimple case. This generalizes earlier work on type A by Brunat, Magaard and Marin. In this…

We prove a Tits alternative theorem for subgroups of finitely generated even Artin groups of FC type (EAFC groups), stating that there exists a finite index subgroup such that every subgroup of it is either finitely generated abelian, or…

We announce an atlas of subgroup lattices of almost simple groups and present two algorithms that were used to produce the atlas.